Implement LSH

algods/algods.py

@@ -1,14 +1,14 @@
 import argparse
-import random
-import time
 import unicodedata
 import sys
 
 import numpy as np
 
-
 SHINGLE_SIZE = 5  # Known as k
-PERMUTATIONS_COUNT = 3
+PERMUTATIONS_COUNT = 800
+BAND_COUNT = 400
+ROWS_PER_BAND = 2
+assert PERMUTATIONS_COUNT == BAND_COUNT * ROWS_PER_BAND
 
 
 def parse_args(argv: dict = None) -> argparse.Namespace:
@@ -64,13 +64,8 @@ def compute_signature_matrix(shingles: np.ndarray, permutations_count: int) -> n
     signature_matrix = np.inf * np.ones((permutations_count, docs_count))
 
     for permutation_id in range(permutations_count):
-        permutation = np.random.permutation(shingles_count)
-
-        for doc_id, doc_shingles in enumerate(shingles.T):
-            for x in permutation:
-                if doc_shingles[x]:
-                    signature_matrix[permutation_id, doc_id] = x
-                    break
+        permutation = np.random.permutation(shingles)
+        signature_matrix[permutation_id] = permutation.argmax(0)
 
     return signature_matrix
 
@@ -91,9 +86,34 @@ def parse(stream, similarity: float) -> None:
     shingles = compute_shingles(docs, SHINGLE_SIZE)
     signature = compute_signature_matrix(shingles, PERMUTATIONS_COUNT)
 
+    candidate_pairs = set()
+
+    for band_id in range(BAND_COUNT):
+        band = signature[band_id * ROWS_PER_BAND:(band_id + 1) * ROWS_PER_BAND]
+
+        buckets = {}
+
+        for doc in range(len(docs)):
+            sign_doc = tuple(band[:, doc])
+            buckets.setdefault(sign_doc, set())
+            buckets[sign_doc].add(doc)
+
+        for bucket in buckets.values():
+            for doc_a in bucket:
+                for doc_b in bucket:
+                    if doc_a != doc_b:
+                        doc_a, doc_b = min(doc_a, doc_b), max(doc_a, doc_b)
+                        candidate_pairs.add((doc_a, doc_b))
+
+    candidate_pairs = sorted(candidate_pairs)
+    for doc_a, doc_b in candidate_pairs:
+        print(doc_a, doc_b)
+
+    exit(1)
+
+    # Calculate true jaccard similarity
     shingles_sets = [set(x for x in range(len(shingles)) if shingles[x, doc_id]) for doc_id in range(len(docs))]
     for i, doc1 in enumerate(shingles_sets):
-        t = time.time()
         for j in range(i + 1, len(docs)):
             doc2 = shingles_sets[j]
             d = jaccard_similarity(doc1, doc2)